The invention concerns the multiresolution reconstruction of a three-dimensional image of an object particularly from a set of two-dimensional projected images of the object obtained for different positions of a camera around the object.
It has a particularly important application in the medical field, in which reconstruction of the internal structures of the patient under examination is undertaken, particularly the reconstruction of angiography images, that is, obtaining images of vasculature opacified by injection of a contrast medium.
The invention can, nevertheless, have applications in other fields, notably, in nondestructive industrial control, in which examinations of the same type as medical examinations are performed.
In the medical field the two-dimensional projected images of the object, a patient""s head, for example, are generally obtained by rotation of an X-ray camera turning around the object.
There are essentially two types of reconstruction algorithms in X-ray imaging.
A first type concerns the so-called algebraic iterative methods of reconstruction.
A second type, with which the invention is concerned, provides for a calculation of filtering and back projection called analytical method. The analytical method uses a mathematical model of the system of acquisition of acquired two-dimensional images. Each pixel of an acquired two-dimensional image contains a gray level which represents the resultant of the intensity of an X-ray having crossed a group of tissues. That statement is then expressed in the form of an analytical equation from which an inverse equation is determined, making it possible to determine a volume representation from gray levels of pixels of two-dimensional images.
The analytical reconstruction of a three-dimensional image essentially uses two stages, a first filtering stage and a second back projection stage. Both stages result from the inverse equation. From a virtual volume, a cube, for example, divided into elementary volume elements called voxels, back projection makes it possible to take each voxel, project the voxel on the acquired two-dimensional images and find the sum of the gray levels of the pixels obtained by projection. The gray level assigned to the voxel is the sum of the gray levels of the pixels obtained by projection.
In general, the methods of reconstruction of analytical type employ an analytical algorithm that is directly applied on the acquired two-dimensional images.
The acquired two-dimensional images generally have a resolution equal to 512, that is, they contain 512 lines and 512 columns of pixels. To take best advantage of the total images acquired in 512 resolution, the image reconstruction algorithm can be applied with a resolution of 512, a treatment would thus be obtained on approximately 134 million (5123) voxels, which is much too great a number, necessitating a long calculation time and, in any case, not very useful, for the vascular structures that it is generally desired to visualize typically occupy approximately 2% to 5% of the virtual volume.
Methods of reconstruction of algebraic type are known, notably, that described in French patent No. 89 16906, which propose applying an iterative algorithm not directly on the acquired two-dimensional images, but on those images after modification. Modification consists of taking an average on each acquired two-dimensional image endowed with a given resolution, called high resolution (HR), so as to obtain an acquired two-dimensional image of lesser resolution called low resolution (LR). The algebraic algorithm is applied on that low-resolution two-dimensional image to form a low-resolution three-dimensional image with a very short calculation time. Then the low-resolution image is transformed into a high-resolution three-dimensional image (identical to the resolution of the initial acquired two-dimensional images) by using complex methods of trilinear interpolation. The algebraic algorithm is then applied by using the three-dimensional image of greater resolution and the initial acquired two-dimensional images (unmodified). That method of reconstruction applies only to algebraic algorithms.
The present invention is to apply the multiresolution technique to analytical type algorithms.
The invention is also intended to reduce the time of calculation of three-dimensional image reconstruction by using an analytical type algorithm.
The invention therefore proposes a method of three-dimensional image reconstruction from a set of two-dimensional images acquired by means of a camera. In order to do so, a subsampling is taken of the set of acquired two-dimensional images so as to reduce the resolution of the acquired two-dimensional images. That stage can be matched to a smoothing stage for which the final image obtained contains a number of pixels less than the initial acquired two-dimensional image.
A first analytical algorithm of three-dimensional image reconstruction from low-resolution (LR) acquired two-dimensional images is then applied in order to obtain a low-resolution three-dimensional image.
A reconstruction support is determined by selecting in the low-resolution three-dimensional image a set of particular voxels.
One then applies a second analytical algorithm of three-dimensional image reconstruction from acquired two-dimensional images and considering only the voxels of the reconstruction support. The first and second analytical algorithms can be identical or different. Preferably, the main characteristic of the first algorithm is speed, the quality of the image obtained being less important.
That method has the advantage of applying an analytical algorithm twice with a calculation time for each application in the order of eight times less than the standard application of an analytical algorithm directly on a high-resolution (HR) acquired two-dimensional image. The first application of the analytical algorithm is faster than a standard application, for the two-dimensional image from which the algorithm is made possesses a reduced resolution. The second application of the analytical algorithm is more rapid than a standard application, for the number of voxels used to reconstruct the high-resolution three-dimensional image is considerably limited.
According to one embodiment of the invention, the subsampling of an acquired two-dimensional image includes obtaining a low-resolution acquired two-dimensional image in which each pixel is composed of several pixels of the initial acquired two-dimensional image with the average gray level of the initial pixels as gray level.
According to one advantageous characteristic of the invention, the first and second analytical algorithms are so-called Feldkamp algorithms. That type of algorithm, well known to the expert, is described in the article xe2x80x9cPractical cone-beam algorithm,xe2x80x9d L. A. FELDKAMP, L. C. DAVIS and J. W. KRESS, Journal Optical Society of America, A/Vol. 1, No. 6, June 1984. In general, Feldkamp""s analytical algorithm mainly comprises a filtering stage and a back projection stage.
The reconstruction support is advantageously determined by applying a threshold on the low-resolution three-dimensional image, so as to maintain a percentage of voxels having the greatest gray levels.
The invention also proposes a method of three-dimensional image reconstruction from a set of acquired two-dimensional images in which:
filtering of the set of acquired two-dimensional images is carried out so as to obtain filtered two-dimensional images,
subsampling of the set of filtered two-dimensional images is carried out so as to reduce the resolution of the filtered two-dimensional images,
a back projection of the subsampled two-dimensional images of low resolution, therefore, is carried out in order to obtain a low-resolution three-dimensional image,
a reconstruction support is determined by selecting in the low-resolution three-dimensional image a set of particular voxels, and
a back projection of the filtered two-dimensional images is carried out by considering only the voxels of the reconstruction support.
The filtering and back project ion stages are preferably carried out by applying Feldkamp""s algorithm. In other words, Feldkamp""s algorithm is applied the first time by inserting a subsampling stage between filtering and back projection. Then Feldkamp""s algorithm is applied a second time by carrying out only the back projection stage. The filtering stage is carried out only in the second application of Feldkamp""s algorithm, for the latter is applied on already filtered images. A time saving is thus obtained by economizing on a filtering stage.